CMU 15-112: Fundamentals of Programming and Computer Science
Class Notes: Functions Redux (part 2)

1. Keyword args (**kwargs)
2. Functions inside functions
3. Closures + Non-local variables
4. Non-local variables fail on setting (use nonlocal)
5. Functions that return functions
6. Function decorators

1. Keyword args (**kwargs)   video
   

   def f(x=1, y=2): return (x,y)
   print(f()) # (1, 2)
   print(f(3)) # (3, 2)
   print(f(y=3)) # (1, 3) [here is where we use a keyword arg]
   
   def f(x, **kwargs): return (x, kwargs)
   print(f(1)) # (1, { })
   print(f(2, y=3, z=4)) # (2, {'z': 4, 'y': 3})

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2. Functions inside functions   video
   

   def f(L):
       def squared(x): return x**2
       return [squared(x) for x in L]
   print(f(range(5)))
   try:
       print(squared(5))
   except:
       print("squared is not defined outside f")

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3. Closures + Non-local variables   video
   

   def f(L):
       myMap = dict()
       def squared(x):
           result = x**2
           myMap[x] = result
           return result
       squaredList = [squared(x) for x in L]
       return myMap
   print(f(range(5)))

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4. Non-local variables fail on setting (use nonlocal)   video
   

   def brokenF(L):
       lastX = 0
       def squared(x):
           result = x**2
           lastX = x
           return result
       squaredList = [squared(x) for x in L]
       return lastX
   print(brokenF(range(5)))
   
   def fixedF(L):
       lastX = 0
       def squared(x):
           nonlocal lastX
           result = x**2
           lastX = x
           return result
       squaredList = [squared(x) for x in L]
       return lastX
   print(fixedF(range(5)))

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5. Functions that return functions   video
   

   def derivativeFn(f):
       def g(x):
           h = 10**-5
           return (f(x+h) - f(x))/h
       return g
   
   def f(x): return 5*x**3 + 10
   fprime1 = derivativeFn(f)
   fprime2 = derivativeFn(fprime1)
   print(f(3))    # 145, 5*x**3 + 10 evaluated at x == 3
   print(fprime1(3)) # about 135, 15*x**2 evaluated at x == 3
   print(fprime2(3)) # about 90, 30*x evaluated at x == 3

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6. Function decorators   video
   

   @derivativeFn
   def h(x): return 5*x**3 + 10
   print(h(3)) # 135, matches fprime1 from above.

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